Do dress modestly. Dubai (and the UAE in general) has a conservative culture, and although strict laws apply to locals and not tourists, men and women should be mindful of the culture and dress accordingly.
Do use plenty of sunscreen. The heat can be sapping!
Do stay hydrated - drink plenty of fluids and carry a water bottle with you at all times
Do cover your head to protect it from the heat - a nice sun hat can save you a lot of agony. Also carry sunglasses so you can enjoy the sights of Dubai in the heat.